×
Gong, Zengtai; Guo, Xiaobin

Inconsistent fuzzy matrix equations and its fuzzy least squares solutions. (English) Zbl 1211.15038

Appl. Math. Modelling 35, No. 3, 1456-1469 (2011).
Summary: The \(m \times n\) inconsistent fuzzy matrix equation \(A\tilde{x}=\tilde{B}\) is investigated. The fuzzy least squares solution and the weak fuzzy least squares solution to the fuzzy matrix equation are expressed by using generalized inverses of the matrix \(S\). The existence condition of strong fuzzy least squares solutions to the fuzzy system is also discussed. Some examples are presented to illustrate the proposed method.

Cited in 7 Documents

MSC:

15B15 Fuzzy matrices
15A24 Matrix equations and identities
65F20 Numerical solutions to overdetermined systems, pseudoinverses

Keywords:

fuzzy numbers; inconsistent fuzzy matrix equations; fuzzy least squares solutions
PDF BibTeX XML Cite
\textit{Z. Gong} and \textit{X. Guo}, Appl. Math. Modelling 35, No. 3, 1456--1469 (2011; Zbl 1211.15038)
Full Text: DOI

References:

[1] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci., 8, 199-249 (1975) · Zbl 0397.68071
[2] Chang, S. S.L.; Zadeh, L. A., On fuzzy mapping and control, IEEE Trans. Syst. Man Cybernet., 2, 30-33 (1972) · Zbl 0305.94001
[3] Dubois, D.; Prade, H., Operations on fuzzy numbers, J. Syst. Sci., 9, 613-626 (1978) · Zbl 0383.94045
[4] Nahmias, S., Fuzzy variables, Fuzzy Sets Syst., 1, 2, 97-111 (1978) · Zbl 0383.03038
[5] Puri, M. L.; Ralescu, D. A., Differentials for fuzzy functions, J. Math. Anal. Appl., 91, 552-558 (1983) · Zbl 0528.54009
[6] Goetschell, R.; Voxman, W., Eigen fuzzy number sets, Fuzzy Sets Syst., 16, 75-85 (1985) · Zbl 0581.04007
[7] Goetschell, R.; Voxman, W., Elementary calculus, Fuzzy Sets Syst., 18, 31-43 (1986)
[8] Wu, C. X.; Ma, M., Embedding problem of fuzzy number space: Part I, Fuzzy Sets Syst., 44, 33-38 (1991) · Zbl 0757.46066
[9] Wu, C. X.; Ma, M., Embedding problem of fuzzy number space: Part III, Fuzzy Sets Syst., 46, 281-286 (1992) · Zbl 0774.54003
[10] Feng, G.; Chen, G., Adaptive control of discrete-time chaotic systems: A fuzzy control approach, Chaos Solitons Fract., 23, 459-467 (2005) · Zbl 1061.93501
[11] Park, J. H., Intuitionistic fuzzy metric space, Chaos Solitons Fract., 22, 1039-1046 (2004) · Zbl 1060.54010
[12] Abbasbandy, S.; Nieto, J. J.; Alavi, M., Turning of reachable set in one dimentional fuzzy differential inclusions, Chaos Solitons Fract., 26, 1337-1341 (2005) · Zbl 1073.65054
[13] Tanaka, Y.; Mizuno, Y.; Kado, T., Chaotic dynamics in the Friedman equation, Chaos Solitons Fract., 24, 407-422 (2005) · Zbl 1070.83535
[14] Friedman, M.; Ma, M.; Kandel, A., Fuzzy linear systems, Fuzzy Sets Syst., 96, 201-209 (1998) · Zbl 0929.15004
[15] Abbasbandy, S.; Ezzati, R.; Afarian, A. J., LU decomposition method for solving fuzzy system of linear equations, Appl. Math. Comput., 172, 633-643 (2006) · Zbl 1088.65023
[16] Abbasbandy, S.; Jafarian, A.; Fzzati, R., Conjugate gradient method for fuzzy symmetric positive definite system of linear equations, Appl. Math. Comput., 171, 1184-1191 (2005) · Zbl 1121.65311
[17] Allahviranloo, T., Numerical methods for fuzzy system of linear equations, Appl. Math. Comput., 153, 493-502 (2004) · Zbl 1067.65040
[18] Allahviranloo, T., Successive over relaxation iterative method for fuzzy system of linear equations, Appl. Math. Comput., 162, 189-196 (2005) · Zbl 1062.65037
[19] Allahviranloo, T., The adomian decomposition method for fuzzy system of linear equations, Appl. Math. Comput., 163, 553-563 (2005) · Zbl 1069.65025
[20] Dehghan, M.; Hashemi, B., Iterative solution of fuzzy linear systems, Appl. Math. Comput., 175, 645-674 (2006) · Zbl 1137.65336
[21] Dehghan, M.; Hashemi, B.; Ghatee, M., Solution of the full fuzzy linear systems using iterative techniques, Chaos Solitons Fract., 34, 316-336 (2007) · Zbl 1144.65021
[22] Asady, B.; Abbasbandy, S.; Alavi, M., Fuzzy general linear systems, Appl. Math. Comput., 169, 34-40 (2005) · Zbl 1119.65325
[23] Wang, K.; Zheng, B., Inconsistent fuzzy linear systems, Appl. Math. Comput., 181, 973-981 (2006) · Zbl 1122.15004
[24] Zheng, B.; Wang, K., General fuzzy linear systems, Appl. Math. Comput., 181, 1276-1286 (2006) · Zbl 1122.15005
[25] Abbasbandy, S.; Otadi, M.; Mosleh, M., Minimal solution of general dual fuzzy linear systems, Chaos Solitons Fract., 29, 638-652 (2008) · Zbl 1146.15002
[26] Zhang, X. D., Matrix Analysis and Applications (2004), Tsinghua and Springer Press: Tsinghua and Springer Press Beijing, (in chinese)
[27] Ben-Israel, A.; Greville, T. N.E., Generalized Inverses: Theory (2003), Springer-Verlag: Springer-Verlag New York · Zbl 1026.15004
[28] Plemmons, R. J., Regular nonnegative matrices, Proceedings of the American Mathematical Society (1973) · Zbl 0273.20051
[29] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic Press: Academic Press New York · Zbl 0484.15016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.